Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.*;

public class Main {
  public static void main(String[] args) throws Exception {
    Scanner sc = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);

    int n = sc.nextInt();
    for (int i = 1; i <= n; i++) {
      int max = 2 * i - 2;
      if(max >= n - 1) {
        out.println(i);
        int row = 1, col = 1;
        while(n-- > 0) {
          out.println(row + " " + col);
          col++;
          if(col == i + 1) {
            row++;
            col--;
          }
        }
        break;
      }
    }

    out.flush();
  }

  static class Scanner {
    StringTokenizer st;
    BufferedReader br;

    public Scanner(InputStream s) {
      br = new BufferedReader(new InputStreamReader(s));
    }

    public Scanner(FileReader f) {
      br = new BufferedReader(f);
    }

    public String next() throws IOException {
      while (st == null || !st.hasMoreTokens())
        st = new StringTokenizer(br.readLine());
      return st.nextToken();
    }

    public int nextInt() throws IOException {
      return Integer.parseInt(next());
    }

    public long nextLong() throws IOException {
      return Long.parseLong(next());
    }

    public String nextLine() throws IOException {
      return br.readLine();
    }

    public double nextDouble() throws IOException {
      String x = next();
      StringBuilder sb = new StringBuilder("0");
      double res = 0, f = 1;
      boolean dec = false, neg = false;
      int start = 0;
      if (x.charAt(0) == '-') {
        neg = true;
        start++;
      }
      for (int i = start; i < x.length(); i++)
        if (x.charAt(i) == '.') {
          res = Long.parseLong(sb.toString());
          sb = new StringBuilder("0");
          dec = true;
        } else {
          sb.append(x.charAt(i));
          if (dec)
            f *= 10;
        }
      res += Long.parseLong(sb.toString()) / f;
      return res * (neg ? -1 : 1);
    }

    public boolean ready() throws IOException {
      return br.ready();
    }

  }
}